You are probably best off into breaking this down into components:
1.
"receive pdf file sent from Angular" looks to me like you want to create a POST request from Angular. So search for that and you will find articles similar to this
AngularJS Http Post Method ($http.post) with Parameters Example - Tutlane[
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2.
... through web API looks like you want this POST request to be processed in Web API as a file upload. Then search for just that and you will find something like
Uploading a File in ASP.Net Web API[
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Now the way I would do this would be to create the Web API file upload component first and use a simple web page with file upload on it to test it out and make sure it is working; and then work on the Angular component to replicate that html form